Annals of Probability

Stochastic calculus for symmetric Markov processes

Z.-Q. Chen, P. J. Fitzsimmons, K. Kuwae, and T.-S. Zhang

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Using time-reversal, we introduce a stochastic integral for zero-energy additive functionals of symmetric Markov processes, extending earlier work of S. Nakao. Various properties of such stochastic integrals are discussed and an Itô formula for Dirichlet processes is obtained.

Article information

Ann. Probab., Volume 36, Number 3 (2008), 931-970.

First available in Project Euclid: 9 April 2008

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Zentralblatt MATH identifier

Primary: 31C25: Dirichlet spaces
Secondary: 60J57: Multiplicative functionals 60J55: Local time and additive functionals 60H05: Stochastic integrals

Symmetric Markov process time reversal stochastic integral generalized Itô formula additive functional martingale additive functional dual additive functional Revuz measure dual predictable projection


Chen, Z.-Q.; Fitzsimmons, P. J.; Kuwae, K.; Zhang, T.-S. Stochastic calculus for symmetric Markov processes. Ann. Probab. 36 (2008), no. 3, 931--970. doi:10.1214/07-AOP347.

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